Spoken dialogues with and between voice agents are becoming increasingly common, yet assessing them for their socially harmful content such as violence, harassment, and hate remains text-centric and fails to account for audio-specific cues and transcription errors. We present LALM-as-a-Judge, the first controlled benchmark and systematic study of large audio-language models (LALMs) as safety judges for multi-turn spoken dialogues. We generate 24,000 unsafe and synthetic spoken dialogues in English that consist of 3-10 turns, by having a single dialogue turn including content with one of 8 harmful categories (e.g., violence) and on one of 5 grades, from very mild to severe. On 160 dialogues, 5 human raters confirmed reliable unsafe detection and a meaningful severity scale. We benchmark three open-source LALMs: Qwen2-Audio, Audio Flamingo 3, and MERaLiON as zero-shot judges that output a scalar safety score in [0,1] across audio-only, transcription-only, or multimodal inputs, along with a transcription-only LLaMA baseline. We measure the judges' sensitivity to detecting unsafe content, the specificity in ordering severity levels, and the stability of the score in dialogue turns. Results reveal architecture- and modality-dependent trade-offs: the most sensitive judge is also the least stable across turns, while stable configurations sacrifice detection of mild harmful content. Transcription quality is a key bottleneck: Whisper-Large may significantly reduce sensitivity for transcription-only modes, while largely preserving severity ordering. Audio becomes crucial when paralinguistic cues or transcription fidelity are category-critical. We summarize all findings and provide actionable guidance for practitioners.